Question: $A$ $B$ $C$ If: $ AC = 45$, $ BC = 4x + 4$, and $ AB = 7x + 8$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 8} + {4x + 4} = {45}$ Combine like terms: $ 11x + 12 = {45}$ Subtract $12$ from both sides: $ 11x = 33$ Divide both sides by $11$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 4({3}) + 4$ Simplify: $ {BC = 12 + 4}$ Simplify to find ${BC}$ : $ {BC = 16}$